Let us first consider the case of muonphilic DM [1]}. The neutrino oscillation pattern as a function of \(A_{\chi }\)  is shown in Fig.  REF . It is evident from Fig. REF  that the oscillation probabilities in DM appears like vacuum oscillations upto \(A_{\chi }\sim 10^{-4}\, \rm eV^{2}\) . Above this value, oscillation probabilities in DM differ significantly from the vacuum scenario. Again above \(A_{\chi }\sim 10^{-2} \,\rm eV^{2}\) , the survival probability of muon neutrinos approaches unity, i.e., the probability of oscillation from muon neutrino to other neutrino flavours and vice versa, becomes zero. Thus \(\nu _{\mu }\)  decouples from the other two neutrino flavours and only \(\nu _{e}-\nu _{\tau }\)  oscillation is possible above this region.
